No, you are right. A 1.75" front level (if it actually even is a true 1.75", usually it is a tad less than advertised), should theoretically only raise the middle of the truck by half of that.
But since the front of the cab is closer to the front wheels than true middle, call it raising the front of the cab by 1". Then add in whatever extra height non-stock tires would add, if you have bigger than stock tires. So most AT4's come with 32" stock tires. If you put 34" aftermarket tires on (for example), you should only gain an inch of actual height from the tires (2 divided by 1).
That would be a full 2 " higher at the front of the cab/hood. Even on a stock/factory lifted AT4, which is 2" over non-AT4 Sierras, adding only 2" to an AT4's height should (and will) fit under a 7' garage door. And even at 7', the actual height of the garage opening is a little less than 7', depending on how the garage door frame was bucked out. Also, often the garage door itself is usually not 100% up to the top of that height. So say, 6'-10.5" for true clearance on a 7' garage door opening with the garage door and bucked out frame. These AT4's will fit in those openings. It will be tight, but they will fit.
BTW, if I ever build another house again (always built my own houses as a builder/contractor), I will NEVER have less than an 8' garage door opening for height. 7' is common, was the norm, but getting less so, for good reason.